Now we move to the case that the data association \(y_t^{k}\)  is unknown and must be established.
Deep learning-based algorithms label each object to be of some class, but do not distinguish between different objects of the same class.
When there are multiple instances of the same object class, such as multiple chairs in a room, possibilities for data association become combinatorial and thus challenging. Instead of relying on a reliable front-end procedure to associate objects, we use a back-end framework to jointly infer the data association and object locations. Note that
Because of the ambiguous data association, the total number of objects \(M\)  is unknown ahead of time, and needs to be established as well.
Nonparametric models are a set of tools that adapt the model complexity to data. It has the embedded mechanism that the model parameters could grow when there are new data being observed. In particular,
Dirichlet Process (DP) is such a nonparametric stochastic process that models discrete distributions but with flexible parameter size. It can be taken as the generalization of a Dirichlet distribution with infinite dimension. Same as Dirichlet distribution is the conjugate prior for a categorical distribution, DP can be viewed as the conjugate prior for infinite, nonparametric discrete distributions [1]}. In this work, we use a Dirichlet Process (DP) as the prior for data associations \(y_t^k\) . In particular, assume at any point, there are \(M\)  objects being detected in total, the probability of \(y_t^k\)  belongs to object \(i\) :
\(p(y_t^k=i) = \text{DP}(i) = \left\lbrace  \begin{array}{ll}\frac{m_i}{\Sigma _i m_i+\alpha } & 1\le i \le M ,\\\frac{\alpha }{\Sigma _i m_i+\alpha } & i=M+1.\end{array}\right.\) 
